Nondifferentiable Dynamic: Two Examples

TL;DR

This paper explores quantum fluctuations of nondifferentiable quantities in gravity, illustrating how such fluctuations can induce spin-like structures, wormholes, and universe nucleation, with probabilities linked to Einstein equations' complexity.

Contribution

It introduces two examples of quantum fluctuations in nondifferentiable quantities within gravity, highlighting their physical implications and connection to computational complexity.

Findings

Quantum interchange of metric components leads to spin-like structures.

Quantum fluctuations can cause universe nucleation with a frozen extra dimension.

Probability of fluctuations relates to Einstein equations' algorithmic complexity.

Abstract

Some nondifferentiable quantities (for example, the metric signature) can be the independent physical degrees of freedom. It is supposed that in quantum gravity these degrees of freedom can fluctuate. Two examples of such quantum fluctuation are considered: a quantum interchange of the sign of two components of the 5D metric and a quantum fluctuation between Euclidean and Lorentzian metrics. The first case leads to a spin-like structure on the throat of composite wormhole and to a possible inner structure of the string. The second case leads to a quantum birth of the non-singular Euclidean Universe with frozen $5^{th}$ dimension. The probability for such quantum fluctuations is connected with an algorithmical complexity of the Einstein equations.